High-Pressure, High-Temperature Single-Crystal Growth, Ab initio Electronic Structure Calculations, and Equation of State of ε-Fe₃N_1+x

The high-pressure behavior of the hard material ε-Fe 3 N 1+ x was studied up to 33 GPa with in situ X-ray diffraction experiments using diamond anvil cells in combination with synchrotron radiation as well as by ex situ high-temperature, high-pressure treatment at 1600(200) K in a two-stage multianvil device with a Walker-type module. Evaluation of the pressure−volume data up to 10 GPa by fitting a Murnaghan-type equation reveals a bulk modulus of B 0 = 172(4) GPa ( B ′ = 5.7, fixed). The calculated bulk modulus (220 GPa) on the basis of density-functional theory (GGA-PAW-PBE) is in satisfying agreement with the experimental one. Single crystals of ε-Fe 3 N 1+ x as obtained by ex situ high-temperature, high-pressure experiments reveal in X-ray diffraction data refinements a structural model of iron atoms in the motif of a hexagonal close packing with occupation of octahedral voids by nitrogen atoms exhibiting long-range order. The preferred structural model is described in space group P 312 ( a = 4.7241(2) Å, c = 4.3862(2) Å, V = 84.773(6) Å 3, Z = 2, R ( F ) = 0.0339, wR ( F 2 ) = 0.0556) and compared to a second model in P 6 3 22. This choice of structural description is corroborated by the results of density-functional calculations. These yield a total energy at 0 K, which is 5 kJ/mol lower for the model in space group P 312 compared to the second best alternative arrangement. Using micro- and nanoindentation techniques, a Vickers hardness of H V = 7.4(10) GPa, a nanoindentation hardness of H = 10.1(8) GPa, as well as a reduced elastic modulus in the amount of E r = 178(11) GPa were measured for ε-Fe 3 N 1+ x single crystals.